Method for determining a hybrid protection radius during the positioning of a carrier and associated determination device

Abstract

Method for determining a hybrid protection radius during carrier positioning and associated determination device. The present invention relates to a method for determining a hybrid protection radius during carrier positioning; the method comprising the following steps: - determination (120) of an effect related to an error in inertial and GNSS measurements; - determination (130) of an effect related to a bounded error in GNSS measurements; - determination (140) of the hybrid protection radius by a value corresponding to the sum of the effects related to the error in inertial and GNSS measurements and to the error in bounded GNSS measurements; wherein the effect related to the error in bounded GNSS measurements is determined by a norm of a zonotope with a generating matrix determined as a function of a vertical protection radius and / or a horizontal protection radius provided by the GNSS signal receiver. Figure for the abstract: Figure 2

Description

Title of the invention: Method for determining a hybrid protection radius during the positioning of a carrier and associated determination device

[0001] The present invention relates to a method for determining a hybrid protection radius during the positioning of a carrier. The present invention also relates to a determination device associated with such a method.

[0002] In particular, the field of the invention is that of inertial navigation using GNSS signals from GNSS systems (Global Navigation Satellite Systems). Such a navigation method is known as "hybrid" navigation because it uses both measurements from inertial devices and GNSS measurements (i.e., GNSS signals from GNSS systems). "Loose coupling" refers to hybridization that uses the GNSS position (and not measurements from each individual satellite) to calculate the hybrid navigation.

[0003] As is known per se, in the case of GNSS-only navigation, the GNSS position error is included with a very high probability within a volume delimited by protection radii determined by the GNSS receiver. Typically, this volume is a cylinder with a height of 2x VPL (Vertical Protection Limit) and a radius of HPL (Horizontal Protection Limit). These protection radii are calculated either using a SBAS (Satellite-Based Augmentation System) or a RAIM (Receiver Autonomous Integrity Monitoring) system.

[0004] In the case of loose hybridization, the GNSS protection radii are no longer suitable for the hybrid position error because the latter is smoothed by the use of the inertial measurement unit and the protection radii must take into account the position error related to the inertial measurement unit.

[0005] The present invention aims to solve this problem and to enable the determination of a hybrid protection radius in the context of inertial navigation using GNSS measurements.

[0006] To this end, the invention aims at a method for determining a hybrid protection radius during the positioning of a carrier, the positioning being determined from inertial measurements and GNSS measurements provided by a GNSS signal receiver;

[0007] the process comprising the following steps:

[0008] - determination of an effect related to an error in inertial and GNSS measurements;

[0009] - determination of an effect related to a bounded error in GNSS measurements;

[0010] - determination of the hybrid protection radius by a value corresponding to the sum of the effects related to the error of inertial and GNSS measurements and to the error of bounded GNSS measurements;

[0011] wherein the effect related to the error of bounded GNSS measurements is determined by a norm of a zonotope with a generating matrix determined as a function of a vertical protection radius and / or a horizontal protection radius provided(s) by the GNSS signal receiver.

[0012] According to other advantageous aspects of the invention, the method comprises one or more of the following features, taken individually or in all technically possible combinations:

[0013] - the effect related to the error of inertial and GNSS measurements is determined statistically; - The dimension of the zonotope is N x P where:

[0014] - N is the hybrid navigation data dimension;

[0015] - P is proportional to the number of columns of the generating matrix of the zonotope;

[0016] - the generating matrix of the zonotope includes an iterative part determined for each new GNSS measurement based on a previous GNSS measurement and a part determined based on the vertical protection radius and / or the horizontal protection radius provided by the GNSS signal receiver;

[0017] - the generating matrix of the zonotope is determined by a propagation phase and a recalibration phase;

[0018] - the bounded GNSS measurement error is written in the form:

[0019] X = Ea

[0020] where:

[0021] - E is the generating matrix of the zonotope;

[0022] - a is a vector of coefficients with a norm less than or equal to 1;

[0023] - the zonotope is a simple zonotope defined by the relation:

[0024] [c + Ea,

[0025] where

[0026] a etc are vectors of coefficients;

[0027] E is the generating matrix of the zonotope.

[0028] - the zonotope is an extended zonotope defined by the relation:

[0029] lEla + E2b, V i |a(-| < 1 and ||^|LH,

[0030] where

[0031] a is a vector of coefficients;

[0032] b is a matrix of type ]7 with each bj of size 2x1;

[0033] £iet E2 are generating matrices of the zonotope.

[0034] The invention also relates to a computer program comprising software instructions which, when executed by a computer, implement the process as defined above.

[0035] The invention also relates to a device for determining a hybrid protection radius, comprising technical means configured to implement the method as defined above.

[0036] The invention will become clearer upon reading the following description, given solely by way of non-limiting example, and made with reference to the drawings in which:

[0037] - [Fig. 1] [Fig. 1] is a schematic view of a determination device according to the invention;

[0038] - [Fig.2] [Fig.2] is a flowchart of a determination process, the process being implemented by the device of [Fig.1].

[0039] We have indeed represented on [Fig.1] a determination device 10 allowing to determine a hybrid protection radius during a positioning of a carrier.

[0040] The carrier is, for example, an aircraft or a vehicle or any other machine capable of flying and / or moving on the Earth's surface. The carrier may, for example, be at least partially manually piloted by a pilot or operator (in the case of an airplane, for example) and / or at least partially automatically piloted (in the case of a drone, for example).

[0041] The carrier includes an inertial measurement unit 12 and at least one GNSS receiver 14.

[0042] The GNSS receiver 14 is configured to generate GNSS measurements from GNSS signals originating from one or more GNSS systems (such as the GPS system, for example). The GNSS measurements include, in particular, a 2D or 3D position of the carrier and its 2D or 3D velocity.

[0043] The GNSS receiver 14 is further configured to determine a vertical protection radius, known as the "VPL value," and / or a horizontal protection radius, known as the "HPL value." These VPL and HPL values ​​are determined using techniques known per se.

[0044] The inertial measurement unit 12 is configured to generate inertial measurements relating to the position of the carrier, such as, for example, the carrier's altitude, its vertical and / or horizontal velocity, its heading, its horizontal position, its attitudes, its 3D position, its 3D velocity, etc. The inertial measurement unit 12 is further configured to generate hybrid navigation data and in particular, a hybrid (2D or 3D) position of the carrier.

[0045] To achieve this, the inertial measurement unit 12 includes an inertial sensor 15 and a hybridization filter 16. The inertial sensor 15, also called the inertial measurement unit, detects movements of the carrier and transmits this information to the hybridization filter 16. The hybridization filter 16 is further connected to the GNSS receiver 14 to receive the data generated by this receiver. The hybridization filter 16 is configured to compile all the received data and to generate hybrid navigation data, including a hybrid (2D or 3D) position of the carrier.

[0046] The determination device 10 comprises an input module 21, a processing module 22 and an output module 23.

[0047] The input module 21 is connected to the inertial measurement unit 12 and the receiver 14, and is capable of acquiring measurements transmitted by these devices. The input module 21 is also capable of transmitting these measurements to the processing module 22.

[0048] The processing module 22 is capable of processing the measurements acquired by the input module 21 in order to determine a hybrid protection radius, as will be explained in more detail later.

[0049] The output module 23 is capable of providing the hybrid protection radius determined by the processing module 22 to any interested system. For example, the output module 23 is capable of providing this radius to a display system and / or a warning system of a pilot or any other operator.

[0050] Each of these modules 21 to 23 includes at least partially one or more programmable logic circuits, such as an FPGA (Field Programmable Gate Array), and / or at least partially software. In the latter case, the software is stored in memory and is executable by one or more processors, advantageously forming part of the determination device 10.

[0051] Advantageously, the determination device 10 is carried on board the carrier. In such a case, the input module 21 is connected to the inertial measurement unit 12 and the receiver 14 by cable. In some examples, at least some of the cable connections are replaced by a wireless connection. In some other examples, the determination device 10 is integrated into the inertial measurement unit 12.

[0052] Alternatively, the determination device 10 is located away from the carrier. In such a case, the input module 21 is connected to the inertial measurement unit 12 and the receiver 14 for communication means known per se.

[0053] The determination device 10 makes it possible to determine a hybrid protection radius by implementing a determination process which will henceforth be explained with reference to [Fig.2] showing a flowchart of its steps.

[0054] Initially, it is assumed that the inertial measurement unit 12 provides hybrid navigation data and the filter gain. The input module 21 then acquires this data during an initial step 110 of the process. Then, this module 21 transmits it to the processing module 22.

[0055] At each instant k() <k< p\ Ie vecteur d’état de dimension N caractérise l’erreur de navigation inertielle.

[0056] This state vector evolves according to the following equivalence:

[0057] x^F^ + eg

[0058] where

[0059] eQ corresponds to the Gaussian noise of a covariance matrix Q; and

[0060] Fk is a propagation matrix.

[0061] The observation model is written in the following form:

[0062] zk+± — Hxk + eR + S

[0063] where

[0064] - ^-k+l is the filter observation linked to the GNSS position;

[0065] - £R corresponds to Gaussian noise with covariance matrix R and S corresponds to a bounded error;

[0066] - H is the observation matrix that links the observation to the state x.

[0067] The estimation x of the state vector can be done using the hybridization filter 16 comprising a propagation phase and a registration phase: 100681

[0069] xMk = F^

[0070] where

[0071] - R is the filter gain.

[0072] The equation for the hybrid navigation error x = X - Xrcst is then the following:

[0073] =(I-KH) xklkA + K£r+KS

[0074] xk+Vk = FkJCk + Sq.

[0075] In the following step 120, the processing module 22 determines the error Xa of hybrid navigation data related to the error of inertial measurements eQ and GNSS. It is assumed in this step that S = 0.

[0076] To do this, the covariance matrix P of X(i) is calculated iteratively as follows:

[0077] pm= (IK.H)Ptl^(I-KJi)T+K£XT 100781 + Q

[0079] The effect of the error of the inertial and GNSS measurements is therefore determined statistically.

[0080] In the next step 130, which can be implemented, for example, in parallel with step 120, the processing module 22 determines the effect of a bounded error Vgdes GNSS measurements. In this step, er = 0 and Eq = 0 are assumed.

[0081] According to the invention, this effect is determined by a standard of a zonotope with a generating matrix determined as a function of at least one of the HPL and VPL values, advantageously of both HPL and VPL values. In particular, when only the horizontal GNSS position is used for hybridization, only the HPL value can be used. When only the vertical GNSS position is used for hybridization, only the VPL value can be used. In the case where the hybridization uses the 3D GNSS position, both the HPL and VPL values ​​can be used.

[0082] Several embodiments of this step 130 are possible.

[0083] According to a first embodiment, the zonotope is a simple zonotope defined by the relation:

[0084] [c+Ea, IHI^l}

[0085] where

[0086] a etc are vectors of coefficients;

[0087] E is the generating matrix.

[0088] In such a case, the hybrid navigation data error Xg related to the bounded error S is written in the following form:

[0089] Xg= Exa.

[0090] where the generating matrix Ex of the simple zonotope is determined in a

[0091] iterative using a calibration phase: E x ^ k =ïU-KH')E^ KE Z \

[0092] and a propagation phase:

[0093] Exji+ = F.Exkjk.

[0094] As illustrated by the recalibration phase, the generating matrix Evkfk includes an iterative part (I-KH)Exj([k_j] linked to the previous times and a part linked to the new GNSS KEZ measurement.

[0095] The part related to the new GNSS measurement is determined by the matrix Ez determined as a function of at least one of the values ​​VPL, HPL, advantageously of both values ​​VPL, HPL.

[0096] For example, this matrix Ez can take the following form:

[0097] HPL 0 0 ■ Ez = 0 HPL 0. 0 0 VPL.

[0098] The upper bound of the error Xg (of size N) or of a part of Xg (of size n < N which is also named Xg for simplification) can be obtained by bounding this error included in Xg according to its dimension n.

[0099] In particular, n can be 1 for one-dimensional data (altitude....) or 2 for two-dimensional data (horizontal position...) in a non-limiting way.

[0100] For example, when n = 1, the error Xg can be bounded as follows: 101011 |X S | s

[0102] where p is the number of columns of the matrix Ex. This number p is, for example, proportional to the number of registration phases carried out to obtain this matrix.

[0103] The number p can be large compared with n. This number p can, for example, be between 100 and 1000.

[0104] When n = 2, the error Xg can be bounded as follows:

[0105] ||

[0106] For n > 2, the error Xg can be bounded in a similar way.

[0107] According to a second embodiment, the zonotope is an extended zonotope defined by the relation:

[0108] + E2b, yi |a,-| < 1 and < 1 j,

[0109] where

[0110] a is a vector of coefficients;

[0111] b is a matrix of type £ j1 with each b{ of size 2x1;

[0112] £jet E2 are generating matrices.

[0113] As in the previous case, the Xg error is written in the following form:

[0114] Xg= Ex.e,

[0115] where Ex is a generator matrix composed of two generator matrices of the extended zonotope, as will be explained below. This composite generator matrix Ex is determined iteratively using a registration phase: 101161 Exkit=[(I-KH)ExM.l K£t]

[0117] and a propagation phase: [01181 E^^FF^.

[0119] In this second embodiment, the composite generating matrix Ex corresponds to the matrix = ^^( 1)^1( 12)^^(2] °ù E^ti) denotes the i-th column of the generating matrix E} and E2(i) denotes the columns 2i- 1 and 2i of the generating matrix E2.

[0120] Furthermore, the matrix Ez corresponds to the matrix:

[0121] [^2 = HPL 0. 0 0 HPL 0 0 ■ 0 VPL.

[0122] With HPL 0 ■ and . Q. ^2 = 0 HPL E\-- 0 0 0 . VPL.

[0123] Finally, the vector e takes the following form:

[0124] e- [^¼ahb%ah, ... ].

[0125] As in the previous case, the upper bound of the error Xg (of size N) or of a part of Xg (of size n < N which is also named Xg for simplification) can be obtained by bounding this error included in Xg according to its dimension n.

[0126] For example, when n = 1, the error Xg can be bounded as follows:

[0127] < |And«| + |E2b\ + <^\E^ I + ll2-

[0128] When n = 2, the error Xg can be bounded as follows:

[0129] ||XS||2< 11^11,+ ||EJ>||2.

[0130] The value 11 E^a 11 can be bounded in the same way as the value 11 Esa 11 in the first embodiment.

[0131] As for the value |lÆ^Il c"c, it can be bounded as follows:

[0132] ^e^^ ll2.2

[0133] With ne, ( i ) 112 2=where ( r> corresponds to the maximum eigenvalue of the matrix Y.

[0134] For n > 2, the error Xg can be bounded in a similar way.

[0135] In the next step 140, the processing module 22 determines the radius of hybrid protection by a value corresponding to the sum of the error Xa linked to the error of the inertial measurements SQ and GNSS and the error Xg linked to the error of the bounded GNSS measurements S.

[0136] During the next step 150, the output module 23 transmits this beam to any interested system.

[0137] It is therefore understood that the present invention has a number of advantages.

[0138] In particular, the invention proposes to determine a hybrid protection radius for hybrid navigation using inertial and GNSS measurements. To this end, it is proposed to separately determine the effect of the error in the inertial measurements and that of a bounded error in the GNSS measurements. To bound the latter, it is proposed to use a zonotope determined iteratively while taking into account the VPL and HPL values ​​classically used to determine the effect of an error during navigation using only GNSS signals.

[0139] Of course, other embodiments are also possible.

Claims

Demands

1. A method for determining a hybrid protection radius during the positioning of a carrier, the positioning being determined from inertial measurements and GNSS measurements provided by a GNSS signal receiver (14); the method comprising the following steps: - determination (120) of an effect related to an error in the inertial and GNSS measurements; - determination (130) of an effect related to a bounded error in the GNSS measurements; - determination (140) of the hybrid protection radius by a value corresponding to the sum of the effects related to the error in the inertial and GNSS measurements and to the error in the bounded GNSS measurements; wherein the effect related to the error in the bounded GNSS measurements is determined by a norm of a zonotope with a generating matrix determined as a function of a vertical protection radius (VPL) and / or a horizontal protection radius (HPL) provided(s) by the GNSS signal receiver (14).

2. A method according to claim 1, wherein the effect related to the error of inertial and GNSS measurements is determined statistically.

3. A method according to claim 1 or 2, wherein the dimension of the zonotope is N x P where: - V is the hybrid navigation data dimension; - P is proportional to the number of columns of the generating matrix of the zonotope.

4. A method according to any one of the preceding claims, wherein the generating matrix of the zonotope comprises an iterative part determined for each new GNSS measurement as a function of a previous GNSS measurement and a part determined as a function of the vertical protection radius (VPL) and / or the horizontal protection radius (HPL) provided(s) by the GNSS signal receiver (14).

5. Method according to claim 4, wherein the generating matrix of the zonotope is determined by a propagation phase and a registration phase.

6. A method according to any one of the preceding claims, wherein the bounded GNSS measurement error is written in the form: X = Ea where: - E is the generating matrix of the zonotope; - a is a vector of coefficients with a norm less than or equal to Q1

7. d 1. A method according to any one of the preceding claims, wherein the zonotope is a simple zonotope defined by the relation: [c+Ea, ^^<1} where a etc are coefficient vectors; E is the generating matrix of the zonotope.

8. A method according to any one of claims 1 to 6, wherein the zonotope is an extended zonotope defined by the relation: [E}a+E2b, Vi < let UèJI< Ij, where a is a vector of coefficients; b is a matrix of type jT with each bt of size 2x1; £\et E2 are generating matrices of the zonotope.

9. A computer program comprising software instructions which, when executed by a computer, implement the method according to any one of the preceding claims.

10. Device for determining a hybrid protection radius, comprising technical means (21, 22, 23) configured to implement the method according to any one of claims 1 to 8.

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